Towards F-transform of a Higher Degree

The aim of this contribution is to show how the Ftransform technique can be generalized from the case of constant components to the case of polynomial components. For this purpose, we choose complete functional spaces with inner products. After a general presentation of Fm-transform where m ≥ 0, a detailed characterization of the F -transform is given. We applied a technique of numeric integration in order to simplify computation of F transform components. The inverse Fm-transform, m ≥ 0, is defined in the same way as the ordinary F-transform. Keywords— F-transform, Fm-transform, fuzzy partition, orthogonal basis, Gaussian quadrature